A kinetic Ising model for dynamical behavior of anisotropic system--its significance in streaming phenomena

A time-delayed kinetic Ising model is constructed for a one-dimensional case in order to study dynamical behaviors of systems including anisotropic interactions between elements. Spin-spin interactions are mediated by a unidirectional signal decaying exponentially with space and time. Non-equilibrium order-disorder transition occurs when the frictional coefficient for signal transmission is varied. Then the model is extended by including a macroscopic field which is produced by local fields caused by spins. The macroscopic field also shows a transition at a certain value of the frictional coefficient. This model well reproduces the features of the transition observed in streaming in the stream cell and Nitella cells.